相关论文: Supporting GENP with Random Multipliers
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
A completely elementary and self-contained proof of convergence of Gaussian multiplicative chaos is given. The argument shows further that the limiting random measure is nontrivial in the entire subcritical phase $(\gamma < \sqrt{2d})$ and…
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…
In this short note we address a gaussian property of normal vectors in random non-Hermitian matrices. The approach uses a simple geometric and comparison technique.
Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are naturally viewed as realizations from random processes; an…
We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends…
In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
Iterative Gaussianization is a fixed-point iteration procedure that can transform any continuous random vector into a Gaussian one. Based on iterative Gaussianization, we propose a new type of normalizing flow model that enables both…
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…
This paper is a continuation of our paper "Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices", J. Stat. Phys. (134), 147--159 (2009), in which we proved the Central Limit Theorem for the matrix elements of…
Let $G, G_1,\dots,G_N$ be independent copies of a standard gaussian random vector in $\mathbb{R}^d$ and denote by $\Gamma = \sum_{i=1}^N \langle G_i,\cdot\rangle e_i$ the standard gaussian ensemble. We show that, for any set $A\subset…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…